A bearing is a machine element that both reduces friction and constrains motion between moving parts. Many types of bearings exist, but the greatest reduction in friction occurs when a magnetic bearing is employed, which supports a load using magnetic levitation. Magnetic bearings permit relative motion with very low friction and mechanical wear, and thus support the highest speeds of all kinds of bearing.
Some magnetic bearings use permanent magnets and do not require input of power, but do require external stabilization due to the limitations described by Earnshaw's Theorem. Most magnetic bearings use attraction or repulsion to achieve levitation. Review of the prior art, however, indicates that magnetic bearings exploiting magnetic reluctance have not previously been described.
One way to asymmetrically focus magnetic flux employs a horseshoe-shaped electromagnetic coil. Another means to asymmetrically focus magnetic flux employs magnetic bearing designs use variations of the Halbach series. The five magnet linear Halbach array is well known to those skilled in the art as a means to asymmetrically focus magnetic flux. A magnet array with as few as three consecutive magnets, however, can also focus magnetic flux asymmetrically so that north and south poles extend parallel to each other from the same side of the array. These three magnets are configured in linear fashion such that the center magnet is rotated 90 degrees relative to the end magnets, and the end magnets are rotated 180 degrees relative to each other. This type of magnet array will be called a reluctance array. Like the Halbach array, the north and south magnetic poles emanate from one side of the reluctance array.
Magnetic reluctance is defined as the resistance to the flow of magnetic flux through a magnetic circuit as determined by the magnetic permeability and arrangement of the materials of the circuit. Magnetic permeability can be thought of as the ability of a material to allow passage of magnetic flux. It is analogous to the concept of conductivity in electricity. Iron, for instance, has a high magnetic permeability whereas air has low magnetic permeability. Magnetic flux will pass through air, just as an electric spark will cross an air gap, but flux passes much more readily through iron.
The components comprising a magnetic circuit tend to act in such a way as to facilitate the flow of magnetic flux through the circuit, and thus minimize reluctance. This principle is most famously illustrated in Tesla's Switched Reluctance Motor. A ferromagnetic rotor is made to rotate between electromagnets of opposite polarity (stator coils). The rotor is compelled to rotate in order to complete a magnetic circuit through the rotor and stator coils. At the point in the rotation where magnetic flux flows most readily, the magnetic circuit is said to be in a state of minimal reluctance. A series of stator coils are configured in a circle, directing magnetic flux inward towards the ferromagnetic rotor. Successively switching the polarity of the stator coils just ahead of the rotating rotor enables continued rotation. Although the Switched Reluctance Motor employs electromagnets, the reluctance principle also applies to magnetic circuits comprising permanent magnets.
Magnetic reluctance has different and advantageous physical and mathematical properties in comparison to the typical magnetic forces of magnetic attraction and repulsion. Whereas the force between magnets falls off with the inverse of the square of the distance between the magnets, reluctance forces increase in a linear fashion with displacement. For example, when two Halbach arrays are magnetically coupled across an air gap of distance X, the force between the arrays is only ¼ as strong at a gap distance of 2X. Experimentation has shown that when two arrays are made to slide past each other at a constant gap distance X, like railway cars on parallel tracks moving in opposite directions, reluctance forces will increase in linear fashion over a short displacement, achieve a maximum, then fall to zero in linear fashion. By way of reference, both a rubber band and a steel spring demonstrate linear force-displacement characteristics. Pulling on either is initially easy but becomes harder the more the rubber band or spring is stretched up to the point of failure.
Reluctance is said to be at a minimum when a magnetic circuit employs materials with the greatest permeability and when the path of the magnetic flux completes the magnetic circuit by the most direct route possible. Reducing air gaps between the magnets and/or ferromagnetic components minimizes reluctance; conversely, reluctance increases whenever a magnetic circuit is disrupted by an increased air gap between the magnetic materials comprising the circuit. Air, having relatively low magnetic permeability, resists the flow of magnetic flux. Directing or focusing the path of flux between the magnetic elements by use of magnet arrays such as the Halbach array facilitates completion of a magnetic circuit and minimizes reluctance.